The Spinnen-Tonnetz: New Musical Dimensions in the 2D Network for Tonal Music Analysis
Résumé
The Polarized Tonnetz developed by Hugues Seress [4] is an innovative two-dimensional representation system for visualizing statically and dynamically some triadic or post-triadic organization, harmonic and tonal paths, as well as tonal regions and musical relations. As for the traditional Tonnetz, the Polarized one relates to transformational design and parsimonious voice leading. Its originality resides however in the introduction of three differentiated criteria concerning the transformation (chromatic distance, modal orientation, polarity) and a fourth parameter: the upward or downward direction of the voice leading. We then enhanced the Polarized Tonnetz with the Planet-4D colorization and animation system developed by Gilles Baroin [1], and finally add a new dynamic graphical layer that illustrates the tonal regions. This paper describes the construction and features of the Spinnen-Tonnetz as well as some musical analysis performed. All videos concerning the construction of the Spinnen-Tonnetz and the musical sample studied are available online at www.MatheMusic.net.